According to an embodiment, a data management system includes an index building unit and a searching unit. The index building unit generates a peripheral vector similar to a case example vector representing a feature vector of data to be stored, and builds index information of enabling identification of the case example vector corresponding to the generated peripheral vector. The searching unit refers to the index information in response to a search request in which a query vector representing an arbitrary feature vector is specified, identifies the case example vector corresponding to the peripheral vector that exactly matches with the query vector, and outputs a search result based on the identified case example vector.